Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 5 5.975085
beta0_pH 7 3.142352
beta1_yellow 4 2.655542
beta0_yellow 4 1.805424
beta1_black 9 1.686350
beta3_yellow 4 1.528670
beta2_yellow 3 1.333292
mu_beta0_pH 2 1.312770
beta1_pH 12 1.293808
beta2_pelagic 5 1.274592
beta2_black 2 1.245202
parameter n badRhat_avg
beta1_pelagic 7 1.243917
beta0_pelagic 5 1.236372
beta3_pelagic 1 1.222106
beta4_yellow 5 1.200738
tau_beta0_pelagic 1 1.174952
beta2_pH 1 1.170728
beta0_black 4 1.156807
tau_beta0_pH 1 1.155881
tau_beta0_yellow 1 1.141739
beta3_black 2 1.129162
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0
beta0_pelagic 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0
beta0_pH 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0
beta0_yellow 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0
beta1_black 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0
beta1_pelagic 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1
beta1_pH 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1
beta1_yellow 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1
beta2_black 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1
beta2_pH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta2_yellow 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1
beta3_black 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta3_pH 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0
beta3_yellow 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1
beta4_yellow 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1
mu_beta0_pH 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.130 0.072 -0.262 -0.133 0.018
mu_bc_H[2] -0.095 0.045 -0.173 -0.099 0.004
mu_bc_H[3] -0.432 0.072 -0.572 -0.433 -0.285
mu_bc_H[4] -0.992 0.189 -1.384 -0.987 -0.633
mu_bc_H[5] 0.965 0.993 -0.173 0.749 3.575
mu_bc_H[6] -2.171 0.328 -2.803 -2.178 -1.509
mu_bc_H[7] -0.460 0.112 -0.686 -0.459 -0.250
mu_bc_H[8] 0.243 0.366 -0.351 0.211 1.096
mu_bc_H[9] -0.295 0.136 -0.561 -0.295 -0.026
mu_bc_H[10] -0.105 0.071 -0.235 -0.107 0.042
mu_bc_H[11] -0.124 0.037 -0.195 -0.123 -0.051
mu_bc_H[12] -0.249 0.103 -0.462 -0.247 -0.047
mu_bc_H[13] -0.140 0.079 -0.295 -0.140 0.014
mu_bc_H[14] -0.303 0.096 -0.497 -0.300 -0.124
mu_bc_H[15] -0.345 0.051 -0.442 -0.346 -0.244
mu_bc_H[16] -0.278 0.376 -0.922 -0.309 0.524
mu_bc_R[1] 1.301 0.148 1.010 1.299 1.598
mu_bc_R[2] 1.452 0.096 1.257 1.454 1.643
mu_bc_R[3] 1.393 0.138 1.114 1.393 1.662
mu_bc_R[4] 0.920 0.201 0.491 0.926 1.287
mu_bc_R[5] 1.145 0.462 0.230 1.147 2.033
mu_bc_R[6] -1.584 0.413 -2.405 -1.577 -0.795
mu_bc_R[7] 0.293 0.197 -0.104 0.298 0.673
mu_bc_R[8] 0.548 0.197 0.146 0.552 0.924
mu_bc_R[9] 0.330 0.209 -0.122 0.345 0.711
mu_bc_R[10] 1.300 0.140 1.003 1.302 1.561
mu_bc_R[11] 1.045 0.101 0.837 1.048 1.243
mu_bc_R[12] 0.836 0.208 0.415 0.839 1.235
mu_bc_R[13] 1.031 0.106 0.822 1.031 1.243
mu_bc_R[14] 0.910 0.140 0.613 0.912 1.179
mu_bc_R[15] 0.767 0.114 0.546 0.769 0.995
mu_bc_R[16] 1.096 0.129 0.833 1.095 1.353
tau_pH[1] 5.260 0.455 4.397 5.245 6.195
tau_pH[2] 1.937 0.734 0.833 2.224 2.992
tau_pH[3] 2.361 0.284 1.873 2.336 2.986
beta0_pH[1,1] 0.507 0.180 0.151 0.516 0.839
beta0_pH[2,1] 1.322 0.177 0.970 1.325 1.669
beta0_pH[3,1] 1.410 0.188 1.006 1.419 1.741
beta0_pH[4,1] 1.573 0.214 1.082 1.588 1.948
beta0_pH[5,1] -0.831 0.300 -1.455 -0.808 -0.331
beta0_pH[6,1] -0.710 0.513 -2.086 -0.601 -0.017
beta0_pH[7,1] 0.150 0.633 -0.971 0.151 0.950
beta0_pH[8,1] -0.672 0.306 -1.461 -0.640 -0.169
beta0_pH[9,1] -0.629 0.295 -1.272 -0.613 -0.112
beta0_pH[10,1] 0.256 0.208 -0.161 0.262 0.650
beta0_pH[11,1] -0.110 0.172 -0.477 -0.100 0.202
beta0_pH[12,1] 0.493 0.182 0.138 0.491 0.857
beta0_pH[13,1] 0.016 0.140 -0.272 0.018 0.289
beta0_pH[14,1] -0.311 0.163 -0.622 -0.308 -0.007
beta0_pH[15,1] -0.017 0.170 -0.395 -0.012 0.300
beta0_pH[16,1] -0.417 0.310 -1.105 -0.380 0.080
beta0_pH[1,2] 2.681 0.266 2.126 2.709 3.125
beta0_pH[2,2] 2.763 0.269 2.053 2.809 3.168
beta0_pH[3,2] 2.552 0.389 1.835 2.530 3.310
beta0_pH[4,2] 2.648 0.351 1.869 2.727 3.192
beta0_pH[5,2] 4.640 1.399 2.819 4.349 8.239
beta0_pH[6,2] 3.084 0.295 2.466 3.093 3.662
beta0_pH[7,2] 1.970 0.202 1.582 1.966 2.401
beta0_pH[8,2] 2.871 0.196 2.496 2.871 3.267
beta0_pH[9,2] 3.400 0.377 2.338 3.426 4.049
beta0_pH[10,2] 3.726 0.242 3.272 3.729 4.195
beta0_pH[11,2] -4.881 0.355 -5.603 -4.876 -4.191
beta0_pH[12,2] -4.805 0.465 -5.761 -4.790 -3.871
beta0_pH[13,2] -4.534 0.486 -5.531 -4.538 -3.517
beta0_pH[14,2] -5.831 0.549 -7.026 -5.793 -4.876
beta0_pH[15,2] -2.571 2.381 -4.821 -4.010 1.086
beta0_pH[16,2] -4.906 0.467 -5.907 -4.887 -4.033
beta0_pH[1,3] 0.559 0.580 -0.737 0.651 1.369
beta0_pH[2,3] 1.914 0.455 0.644 2.045 2.432
beta0_pH[3,3] 2.215 0.386 1.308 2.319 2.706
beta0_pH[4,3] 2.692 0.461 1.345 2.837 3.206
beta0_pH[5,3] 1.078 1.807 -1.724 0.835 5.301
beta0_pH[6,3] -0.755 1.058 -2.799 -0.873 1.430
beta0_pH[7,3] -2.217 0.649 -3.725 -2.161 -1.087
beta0_pH[8,3] 0.261 0.197 -0.133 0.262 0.641
beta0_pH[9,3] -0.990 0.712 -2.748 -0.764 -0.085
beta0_pH[10,3] -0.239 0.993 -2.405 -0.014 1.064
beta0_pH[11,3] -0.205 0.330 -0.847 -0.207 0.456
beta0_pH[12,3] -0.904 0.344 -1.613 -0.881 -0.296
beta0_pH[13,3] -0.137 0.303 -0.746 -0.133 0.444
beta0_pH[14,3] -0.277 0.264 -0.794 -0.275 0.258
beta0_pH[15,3] -0.766 0.286 -1.378 -0.748 -0.243
beta0_pH[16,3] -0.401 0.286 -0.987 -0.398 0.144
beta1_pH[1,1] 3.125 0.318 2.539 3.111 3.804
beta1_pH[2,1] 2.210 0.278 1.719 2.193 2.810
beta1_pH[3,1] 2.019 0.289 1.521 1.998 2.706
beta1_pH[4,1] 2.397 0.346 1.838 2.363 3.178
beta1_pH[5,1] 2.257 0.368 1.673 2.209 3.063
beta1_pH[6,1] 3.989 1.248 2.340 3.710 7.256
beta1_pH[7,1] 7.858 13.609 0.380 2.368 49.231
beta1_pH[8,1] 4.137 1.081 2.582 3.919 6.653
beta1_pH[9,1] 2.298 0.391 1.624 2.255 3.172
beta1_pH[10,1] 2.352 0.295 1.784 2.350 2.963
beta1_pH[11,1] 3.289 0.210 2.905 3.282 3.737
beta1_pH[12,1] 2.542 0.212 2.116 2.544 2.957
beta1_pH[13,1] 2.960 0.206 2.561 2.954 3.395
beta1_pH[14,1] 3.418 0.214 3.025 3.417 3.843
beta1_pH[15,1] 2.519 0.218 2.106 2.517 2.967
beta1_pH[16,1] 4.051 0.576 3.169 3.963 5.419
beta1_pH[1,2] 2.273 7.623 0.001 0.835 16.683
beta1_pH[2,2] 2.257 7.444 0.001 0.764 13.085
beta1_pH[3,2] 1.344 4.806 0.002 1.117 2.372
beta1_pH[4,2] 2.502 10.026 0.002 0.916 13.005
beta1_pH[5,2] 0.515 1.851 0.000 0.001 7.713
beta1_pH[6,2] 0.328 1.247 0.000 0.002 2.222
beta1_pH[7,2] 0.038 0.230 0.000 0.001 0.405
beta1_pH[8,2] 0.035 0.189 0.000 0.001 0.321
beta1_pH[9,2] 0.193 0.895 0.000 0.001 1.771
beta1_pH[10,2] 1.122 2.818 0.000 0.002 9.707
beta1_pH[11,2] 6.739 0.393 6.003 6.721 7.512
beta1_pH[12,2] 6.506 0.535 5.514 6.486 7.657
beta1_pH[13,2] 6.873 0.551 5.678 6.902 7.904
beta1_pH[14,2] 7.465 0.561 6.471 7.429 8.628
beta1_pH[15,2] 6.817 0.899 4.916 6.753 9.003
beta1_pH[16,2] 7.480 0.506 6.482 7.484 8.472
beta1_pH[1,3] 3.000 1.156 1.573 2.718 6.031
beta1_pH[2,3] 2.501 11.603 0.000 0.489 18.438
beta1_pH[3,3] 9.852 78.157 0.000 0.422 14.078
beta1_pH[4,3] 1.910 7.232 0.000 0.332 15.787
beta1_pH[5,3] 3.941 3.717 1.594 3.190 10.682
beta1_pH[6,3] 2.715 1.060 1.146 2.622 4.866
beta1_pH[7,3] 3.071 0.649 1.982 3.014 4.577
beta1_pH[8,3] 2.825 0.365 2.149 2.817 3.534
beta1_pH[9,3] 3.065 0.730 2.095 2.887 4.858
beta1_pH[10,3] 3.656 1.064 2.248 3.387 6.018
beta1_pH[11,3] 2.793 0.386 2.040 2.781 3.588
beta1_pH[12,3] 4.168 0.431 3.381 4.153 5.059
beta1_pH[13,3] 1.750 0.335 1.104 1.749 2.435
beta1_pH[14,3] 2.544 0.334 1.897 2.539 3.222
beta1_pH[15,3] 2.178 0.373 1.488 2.165 2.988
beta1_pH[16,3] 1.836 0.319 1.230 1.819 2.479
beta2_pH[1,1] 0.466 0.117 0.287 0.450 0.732
beta2_pH[2,1] 0.545 0.242 0.246 0.500 1.081
beta2_pH[3,1] 0.597 0.391 0.228 0.517 1.501
beta2_pH[4,1] 0.459 0.186 0.211 0.434 0.853
beta2_pH[5,1] 1.559 1.287 0.245 1.253 4.705
beta2_pH[6,1] 0.183 0.069 0.081 0.172 0.345
beta2_pH[7,1] -0.724 1.688 -5.352 0.018 1.258
beta2_pH[8,1] 0.244 0.097 0.117 0.224 0.488
beta2_pH[9,1] 0.449 0.260 0.181 0.401 0.959
beta2_pH[10,1] 0.631 0.331 0.294 0.561 1.357
beta2_pH[11,1] 0.772 0.198 0.470 0.749 1.260
beta2_pH[12,1] 1.335 0.468 0.746 1.236 2.467
beta2_pH[13,1] 0.747 0.217 0.426 0.720 1.272
beta2_pH[14,1] 0.831 0.198 0.535 0.803 1.311
beta2_pH[15,1] 0.804 0.291 0.409 0.749 1.527
beta2_pH[16,1] 0.381 0.174 0.179 0.336 0.826
beta2_pH[1,2] -2.013 4.085 -10.236 -2.071 6.175
beta2_pH[2,2] -2.746 3.796 -10.210 -2.745 5.288
beta2_pH[3,2] -3.588 2.983 -10.421 -3.155 1.755
beta2_pH[4,2] -3.554 3.086 -10.532 -3.099 1.350
beta2_pH[5,2] -0.376 4.354 -8.676 -0.501 8.215
beta2_pH[6,2] -0.872 4.262 -8.939 -1.112 7.834
beta2_pH[7,2] -0.650 4.374 -8.751 -0.914 8.460
beta2_pH[8,2] -0.539 4.463 -8.926 -0.762 8.875
beta2_pH[9,2] -0.545 4.394 -8.600 -0.950 8.765
beta2_pH[10,2] -1.016 4.395 -9.334 -1.313 7.902
beta2_pH[11,2] -7.194 2.666 -13.696 -6.722 -3.303
beta2_pH[12,2] -4.868 2.935 -11.460 -4.591 -0.757
beta2_pH[13,2] -4.899 2.628 -11.172 -4.389 -1.528
beta2_pH[14,2] -5.710 2.597 -12.073 -5.217 -2.070
beta2_pH[15,2] -6.753 2.731 -13.014 -6.283 -2.540
beta2_pH[16,2] -7.093 2.607 -13.495 -6.640 -3.354
beta2_pH[1,3] 1.492 2.133 0.140 0.495 8.018
beta2_pH[2,3] 0.577 3.544 -6.868 0.582 7.919
beta2_pH[3,3] -0.579 3.755 -8.204 -0.598 7.734
beta2_pH[4,3] 0.278 3.693 -7.709 0.235 8.320
beta2_pH[5,3] 3.628 2.939 -0.284 3.158 10.576
beta2_pH[6,3] 3.627 2.942 0.021 3.167 10.572
beta2_pH[7,3] 3.443 2.670 0.515 2.670 10.333
beta2_pH[8,3] 5.021 2.670 0.918 4.746 11.188
beta2_pH[9,3] 3.103 2.812 0.296 2.465 9.752
beta2_pH[10,3] 2.271 2.563 0.305 0.857 8.750
beta2_pH[11,3] -1.842 1.212 -5.205 -1.551 -0.597
beta2_pH[12,3] -1.980 1.031 -4.723 -1.730 -0.931
beta2_pH[13,3] -2.421 1.568 -6.746 -1.977 -0.758
beta2_pH[14,3] -2.348 1.500 -6.762 -1.933 -0.880
beta2_pH[15,3] -2.445 1.481 -6.765 -2.004 -0.968
beta2_pH[16,3] -2.521 1.684 -7.319 -2.009 -0.874
beta3_pH[1,1] 35.831 0.818 34.298 35.797 37.477
beta3_pH[2,1] 33.479 1.172 31.505 33.386 36.077
beta3_pH[3,1] 33.811 1.070 31.729 33.794 36.024
beta3_pH[4,1] 33.899 1.223 31.677 33.822 36.522
beta3_pH[5,1] 27.829 1.202 26.510 27.521 31.354
beta3_pH[6,1] 38.873 3.166 32.808 38.717 45.026
beta3_pH[7,1] 27.856 9.109 18.223 24.324 45.415
beta3_pH[8,1] 40.266 2.175 36.410 40.073 44.871
beta3_pH[9,1] 30.674 1.576 28.044 30.544 34.002
beta3_pH[10,1] 32.697 0.909 31.019 32.674 34.539
beta3_pH[11,1] 30.323 0.486 29.380 30.327 31.298
beta3_pH[12,1] 30.182 0.408 29.341 30.184 30.952
beta3_pH[13,1] 33.215 0.564 32.186 33.193 34.376
beta3_pH[14,1] 32.073 0.448 31.233 32.061 33.013
beta3_pH[15,1] 31.275 0.625 30.114 31.271 32.545
beta3_pH[16,1] 32.192 1.014 30.502 32.065 34.486
beta3_pH[1,2] 29.713 8.580 18.544 27.626 44.410
beta3_pH[2,2] 25.590 7.033 18.259 22.710 43.579
beta3_pH[3,2] 38.988 6.560 20.158 41.596 44.376
beta3_pH[4,2] 32.300 8.370 19.146 30.212 44.357
beta3_pH[5,2] 29.750 7.971 18.444 28.785 44.766
beta3_pH[6,2] 30.919 7.716 18.479 31.455 44.809
beta3_pH[7,2] 30.030 7.891 18.517 29.280 44.890
beta3_pH[8,2] 30.043 8.074 18.452 28.950 44.844
beta3_pH[9,2] 30.749 8.478 18.451 29.458 45.221
beta3_pH[10,2] 29.750 7.242 18.641 29.298 44.691
beta3_pH[11,2] 43.404 0.166 43.130 43.386 43.747
beta3_pH[12,2] 43.202 0.229 42.753 43.176 43.720
beta3_pH[13,2] 43.809 0.193 43.292 43.851 44.101
beta3_pH[14,2] 43.351 0.196 43.074 43.313 43.812
beta3_pH[15,2] 35.680 10.939 18.342 43.272 43.713
beta3_pH[16,2] 43.503 0.174 43.188 43.502 43.831
beta3_pH[1,3] 38.711 2.172 34.186 39.217 42.767
beta3_pH[2,3] 30.610 7.690 18.606 30.930 44.765
beta3_pH[3,3] 31.482 8.974 18.373 31.727 44.463
beta3_pH[4,3] 28.055 7.661 18.343 26.218 44.747
beta3_pH[5,3] 26.665 6.425 18.370 25.408 41.963
beta3_pH[6,3] 27.166 6.224 18.616 25.797 43.932
beta3_pH[7,3] 26.490 1.019 24.730 26.360 28.859
beta3_pH[8,3] 41.497 0.335 40.924 41.488 42.054
beta3_pH[9,3] 32.456 1.762 28.086 33.228 34.229
beta3_pH[10,3] 34.702 1.539 31.462 35.068 36.738
beta3_pH[11,3] 41.812 0.781 40.215 41.872 43.188
beta3_pH[12,3] 41.743 0.373 41.013 41.744 42.480
beta3_pH[13,3] 42.693 0.823 41.153 42.693 44.363
beta3_pH[14,3] 41.088 0.566 39.887 41.111 42.135
beta3_pH[15,3] 42.575 0.604 41.324 42.620 43.644
beta3_pH[16,3] 42.874 0.709 41.345 42.950 44.107
beta0_pelagic[1] 1.886 0.443 0.847 2.049 2.400
beta0_pelagic[2] 1.233 0.429 0.071 1.387 1.697
beta0_pelagic[3] 0.195 0.331 -0.643 0.248 0.723
beta0_pelagic[4] 0.260 0.512 -1.389 0.319 1.057
beta0_pelagic[5] 0.080 1.483 -3.179 0.959 1.461
beta0_pelagic[6] 1.143 0.499 -0.158 1.326 1.689
beta0_pelagic[7] 1.579 0.148 1.299 1.583 1.850
beta0_pelagic[8] 1.708 0.166 1.403 1.714 1.974
beta0_pelagic[9] 2.182 0.784 0.123 2.485 2.939
beta0_pelagic[10] 2.544 0.157 2.217 2.556 2.816
beta0_pelagic[11] -0.244 0.531 -1.357 -0.160 0.634
beta0_pelagic[12] 1.690 0.138 1.426 1.688 1.965
beta0_pelagic[13] 0.331 0.182 -0.079 0.346 0.651
beta0_pelagic[14] -0.169 0.302 -0.886 -0.127 0.319
beta0_pelagic[15] -0.268 0.122 -0.514 -0.266 -0.030
beta0_pelagic[16] 0.189 0.334 -0.569 0.281 0.639
beta1_pelagic[1] 0.359 0.447 0.000 0.146 1.412
beta1_pelagic[2] 0.326 0.438 0.000 0.119 1.512
beta1_pelagic[3] 0.882 0.453 0.264 0.796 2.106
beta1_pelagic[4] 0.916 0.546 0.000 0.871 2.634
beta1_pelagic[5] 1.172 1.585 0.000 0.028 4.596
beta1_pelagic[6] 0.442 0.623 0.000 0.030 1.965
beta1_pelagic[7] 2.641 6.051 0.000 0.023 15.262
beta1_pelagic[8] 1.307 4.539 0.000 0.004 21.143
beta1_pelagic[9] 0.705 0.968 0.000 0.287 3.360
beta1_pelagic[10] 0.221 0.713 0.000 0.004 2.460
beta1_pelagic[11] 4.587 1.399 2.318 4.407 7.622
beta1_pelagic[12] 2.798 0.299 2.229 2.797 3.383
beta1_pelagic[13] 2.737 0.649 1.709 2.632 4.175
beta1_pelagic[14] 4.722 1.158 3.016 4.507 7.360
beta1_pelagic[15] 2.929 0.260 2.413 2.936 3.431
beta1_pelagic[16] 3.966 1.088 2.745 3.505 6.534
beta2_pelagic[1] 1.723 2.469 -2.670 1.257 7.560
beta2_pelagic[2] 1.845 2.691 -4.333 1.660 7.036
beta2_pelagic[3] 1.790 1.697 0.105 1.308 6.394
beta2_pelagic[4] 2.573 2.240 0.178 1.910 7.415
beta2_pelagic[5] -1.133 4.121 -8.786 -1.811 7.269
beta2_pelagic[6] 1.063 4.027 -7.996 1.124 8.974
beta2_pelagic[7] -1.307 4.460 -9.863 -1.613 7.863
beta2_pelagic[8] -0.540 4.255 -9.183 -0.735 7.960
beta2_pelagic[9] 0.972 3.951 -7.642 0.901 8.939
beta2_pelagic[10] -0.133 4.312 -8.997 -0.095 8.185
beta2_pelagic[11] 0.505 1.161 0.085 0.187 4.104
beta2_pelagic[12] 4.450 2.191 1.326 4.056 9.794
beta2_pelagic[13] 0.773 0.839 0.213 0.544 2.631
beta2_pelagic[14] 0.284 0.112 0.144 0.264 0.537
beta2_pelagic[15] 4.724 2.078 1.556 4.511 9.975
beta2_pelagic[16] 2.454 2.624 0.177 1.184 8.797
beta3_pelagic[1] 26.545 7.124 18.348 23.909 44.058
beta3_pelagic[2] 27.327 8.136 18.270 24.260 44.805
beta3_pelagic[3] 29.789 4.348 22.736 29.569 41.726
beta3_pelagic[4] 26.002 3.856 20.484 25.674 39.073
beta3_pelagic[5] 35.748 9.959 18.773 38.156 45.993
beta3_pelagic[6] 30.446 6.981 18.779 29.907 44.548
beta3_pelagic[7] 26.865 8.034 18.515 23.972 44.574
beta3_pelagic[8] 28.409 8.028 18.336 26.381 44.651
beta3_pelagic[9] 29.747 6.852 18.855 28.371 44.276
beta3_pelagic[10] 28.922 8.215 18.377 27.363 44.698
beta3_pelagic[11] 42.687 2.130 37.683 42.960 45.835
beta3_pelagic[12] 43.462 0.254 43.012 43.452 43.925
beta3_pelagic[13] 42.492 1.209 40.166 42.464 44.999
beta3_pelagic[14] 42.689 1.817 38.918 42.702 45.755
beta3_pelagic[15] 43.174 0.230 42.622 43.183 43.580
beta3_pelagic[16] 43.085 1.016 40.590 43.199 45.283
mu_beta0_pelagic[1] 0.819 0.852 -0.959 0.853 2.417
mu_beta0_pelagic[2] 1.483 0.733 -0.337 1.632 2.576
mu_beta0_pelagic[3] 0.250 0.510 -0.817 0.268 1.202
tau_beta0_pelagic[1] 1.473 4.059 0.062 0.690 6.577
tau_beta0_pelagic[2] 1.582 1.985 0.076 0.975 6.349
tau_beta0_pelagic[3] 1.358 1.037 0.164 1.091 4.003
beta0_yellow[1] -0.542 0.185 -0.985 -0.524 -0.241
beta0_yellow[2] 0.461 0.295 -0.343 0.505 0.796
beta0_yellow[3] -0.295 0.173 -0.638 -0.294 0.039
beta0_yellow[4] 0.807 0.337 -0.266 0.878 1.206
beta0_yellow[5] -1.255 0.425 -2.106 -1.265 -0.409
beta0_yellow[6] 0.559 0.451 -0.117 0.425 1.366
beta0_yellow[7] 0.968 0.389 -0.415 1.035 1.351
beta0_yellow[8] 0.748 0.612 -1.192 0.946 1.280
beta0_yellow[9] -0.079 0.302 -0.646 -0.070 0.445
beta0_yellow[10] 0.232 0.151 -0.067 0.234 0.525
beta0_yellow[11] -2.027 0.441 -2.831 -2.048 -1.111
beta0_yellow[12] -3.654 0.420 -4.511 -3.639 -2.874
beta0_yellow[13] -3.728 0.453 -4.774 -3.690 -2.915
beta0_yellow[14] -2.238 0.483 -3.180 -2.228 -1.288
beta0_yellow[15] -2.834 0.432 -3.779 -2.820 -2.007
beta0_yellow[16] -2.479 0.441 -3.347 -2.476 -1.573
beta1_yellow[1] 0.483 0.549 0.000 0.343 1.786
beta1_yellow[2] 1.190 0.753 0.598 1.034 3.831
beta1_yellow[3] 0.643 0.259 0.047 0.652 1.117
beta1_yellow[4] 1.464 0.852 0.648 1.213 4.113
beta1_yellow[5] 3.197 2.131 1.103 2.974 6.034
beta1_yellow[6] 1.523 1.100 0.000 2.028 2.902
beta1_yellow[7] 3.571 5.219 0.000 2.362 17.611
beta1_yellow[8] 1.538 1.873 0.000 1.085 7.168
beta1_yellow[9] 1.495 0.457 0.744 1.457 2.383
beta1_yellow[10] 2.363 0.500 1.526 2.327 3.407
beta1_yellow[11] 2.164 0.429 1.330 2.183 2.973
beta1_yellow[12] 2.456 0.432 1.665 2.438 3.352
beta1_yellow[13] 2.860 0.458 2.033 2.822 3.906
beta1_yellow[14] 2.294 0.483 1.371 2.276 3.279
beta1_yellow[15] 2.122 0.431 1.322 2.098 3.022
beta1_yellow[16] 2.237 0.448 1.338 2.237 3.125
beta2_yellow[1] -2.829 3.030 -9.895 -2.310 2.807
beta2_yellow[2] -3.122 2.672 -9.372 -2.440 -0.084
beta2_yellow[3] -3.062 2.390 -8.745 -2.548 -0.176
beta2_yellow[4] -2.620 2.664 -9.326 -1.730 -0.082
beta2_yellow[5] -4.163 2.940 -10.976 -3.704 -0.444
beta2_yellow[6] 2.301 3.680 -6.469 2.481 9.289
beta2_yellow[7] -2.815 4.154 -10.762 -3.023 6.032
beta2_yellow[8] -1.415 4.239 -9.830 -1.367 7.598
beta2_yellow[9] 3.791 2.484 0.280 3.280 9.686
beta2_yellow[10] -3.776 2.514 -10.354 -3.124 -0.725
beta2_yellow[11] -4.134 2.298 -10.256 -3.693 -1.284
beta2_yellow[12] -4.331 2.108 -9.404 -3.925 -1.476
beta2_yellow[13] -4.208 1.985 -9.242 -3.779 -1.593
beta2_yellow[14] -4.355 2.269 -9.798 -3.925 -1.215
beta2_yellow[15] -3.867 1.989 -8.725 -3.492 -1.186
beta2_yellow[16] -4.326 1.927 -8.640 -4.034 -1.555
beta3_yellow[1] 27.408 7.590 18.316 24.842 44.526
beta3_yellow[2] 28.869 2.184 22.043 28.868 32.610
beta3_yellow[3] 32.875 3.087 24.302 32.934 39.011
beta3_yellow[4] 28.888 3.706 21.120 27.960 36.195
beta3_yellow[5] 33.263 1.789 29.360 33.390 35.506
beta3_yellow[6] 36.739 6.159 19.920 39.436 42.889
beta3_yellow[7] 23.974 6.976 18.461 20.404 43.414
beta3_yellow[8] 26.329 6.542 18.335 24.877 43.683
beta3_yellow[9] 37.730 1.562 36.069 37.579 42.337
beta3_yellow[10] 29.295 0.649 27.801 29.386 30.191
beta3_yellow[11] 45.321 0.526 44.080 45.413 45.977
beta3_yellow[12] 43.331 0.391 42.580 43.317 44.145
beta3_yellow[13] 44.865 0.370 44.061 44.937 45.482
beta3_yellow[14] 44.285 1.001 43.188 44.269 45.816
beta3_yellow[15] 45.225 0.554 44.128 45.253 45.973
beta3_yellow[16] 44.580 0.615 43.483 44.570 45.800
mu_beta0_yellow[1] 0.099 0.554 -1.014 0.104 1.216
mu_beta0_yellow[2] 0.191 0.513 -0.909 0.207 1.197
mu_beta0_yellow[3] -2.504 0.627 -3.481 -2.596 -0.956
tau_beta0_yellow[1] 2.191 4.970 0.089 1.144 8.531
tau_beta0_yellow[2] 1.224 1.321 0.124 0.908 4.296
tau_beta0_yellow[3] 1.547 2.032 0.103 0.959 6.728
beta0_black[1] 0.154 0.157 -0.192 0.160 0.448
beta0_black[2] 1.889 0.148 1.585 1.899 2.138
beta0_black[3] 1.307 0.144 1.050 1.310 1.570
beta0_black[4] 2.014 0.420 1.018 2.052 2.578
beta0_black[5] 1.674 2.001 -2.670 1.723 5.956
beta0_black[6] 1.654 2.127 -2.913 1.669 6.109
beta0_black[7] 1.677 2.107 -3.003 1.683 6.336
beta0_black[8] 1.236 0.239 0.776 1.244 1.681
beta0_black[9] 2.404 0.282 1.808 2.420 2.894
beta0_black[10] 1.452 0.155 1.193 1.453 1.720
beta0_black[11] 3.444 0.253 3.052 3.468 3.772
beta0_black[12] 4.481 0.194 4.100 4.486 4.854
beta0_black[13] -0.053 0.234 -0.517 -0.052 0.408
beta0_black[14] 2.143 0.631 0.495 2.290 2.849
beta0_black[15] 1.290 0.150 1.003 1.288 1.582
beta0_black[16] 4.242 0.270 3.859 4.266 4.565
beta2_black[1] 0.271 3.145 -6.120 0.135 6.870
beta2_black[2] -0.271 3.065 -6.733 -0.381 6.214
beta2_black[3] -0.312 2.603 -5.450 -0.489 4.796
beta2_black[4] -0.996 2.244 -6.128 -0.845 3.665
beta2_black[5] -0.282 3.411 -7.359 -0.351 6.945
beta2_black[6] -0.240 3.385 -7.242 -0.287 7.062
beta2_black[7] -0.210 3.324 -6.978 -0.302 6.740
beta2_black[8] -1.008 3.461 -7.920 -1.078 6.024
beta2_black[9] -0.302 3.280 -6.856 -0.399 6.764
beta2_black[10] -0.475 3.169 -6.904 -0.571 6.056
beta2_black[11] -1.356 2.491 -6.438 -1.327 4.385
beta2_black[12] -2.603 1.607 -6.392 -2.284 -0.455
beta2_black[13] -2.197 1.630 -6.861 -1.731 -0.516
beta2_black[14] -1.563 1.757 -6.028 -1.084 -0.065
beta2_black[15] -1.366 2.515 -6.742 -1.399 4.344
beta2_black[16] -1.268 2.228 -5.417 -1.396 3.964
beta3_black[1] 31.743 8.390 18.548 31.197 44.779
beta3_black[2] 30.026 7.915 18.375 29.234 44.831
beta3_black[3] 30.137 8.001 18.488 29.441 44.914
beta3_black[4] 32.158 5.124 19.562 32.800 41.925
beta3_black[5] 30.015 7.888 18.424 29.210 45.148
beta3_black[6] 29.867 7.935 18.313 28.868 44.841
beta3_black[7] 29.863 7.866 18.435 28.995 44.695
beta3_black[8] 28.447 7.857 18.589 25.618 44.477
beta3_black[9] 30.195 8.047 18.398 29.413 45.041
beta3_black[10] 29.401 8.163 18.458 27.775 44.875
beta3_black[11] 30.998 7.739 18.551 30.783 44.997
beta3_black[12] 32.516 1.621 26.921 32.872 33.800
beta3_black[13] 39.293 0.695 37.707 39.359 40.490
beta3_black[14] 36.853 5.625 19.842 38.402 44.239
beta3_black[15] 31.572 7.898 18.591 31.954 45.018
beta3_black[16] 31.108 7.974 18.639 30.815 45.175
beta4_black[1] -0.280 0.183 -0.643 -0.282 0.080
beta4_black[2] 0.250 0.176 -0.090 0.248 0.590
beta4_black[3] -0.939 0.188 -1.303 -0.937 -0.571
beta4_black[4] 0.526 0.227 0.084 0.527 0.978
beta4_black[5] 0.214 2.358 -4.320 0.144 5.232
beta4_black[6] 0.232 2.317 -4.513 0.191 4.781
beta4_black[7] 0.192 2.333 -4.288 0.148 4.575
beta4_black[8] -0.666 0.372 -1.416 -0.656 0.041
beta4_black[9] 1.459 1.008 -0.117 1.350 3.731
beta4_black[10] 0.024 0.181 -0.320 0.026 0.377
beta4_black[11] -0.697 0.208 -1.102 -0.699 -0.287
beta4_black[12] 0.300 0.328 -0.299 0.285 0.976
beta4_black[13] -1.196 0.220 -1.645 -1.195 -0.774
beta4_black[14] -0.129 0.232 -0.556 -0.133 0.327
beta4_black[15] -0.897 0.209 -1.316 -0.897 -0.496
beta4_black[16] -0.601 0.228 -1.059 -0.597 -0.160
mu_beta0_black[1] 1.332 0.879 -0.437 1.334 3.069
mu_beta0_black[2] 1.648 1.013 -0.531 1.662 3.718
mu_beta0_black[3] 2.562 1.012 0.404 2.573 4.599
tau_beta0_black[1] 0.960 1.000 0.061 0.654 3.695
tau_beta0_black[2] 2.016 4.822 0.055 0.783 10.686
tau_beta0_black[3] 0.254 0.173 0.052 0.213 0.708
beta0_dsr[11] -2.909 0.284 -3.467 -2.908 -2.343
beta0_dsr[12] 4.525 0.271 4.011 4.521 5.062
beta0_dsr[13] -1.338 0.321 -1.952 -1.319 -0.791
beta0_dsr[14] -3.683 0.500 -4.664 -3.669 -2.732
beta0_dsr[15] -1.930 0.267 -2.465 -1.920 -1.431
beta0_dsr[16] -2.981 0.354 -3.680 -2.981 -2.285
beta1_dsr[11] 4.845 0.296 4.258 4.840 5.435
beta1_dsr[12] 7.084 15.865 2.253 5.057 21.852
beta1_dsr[13] 2.854 0.359 2.279 2.838 3.453
beta1_dsr[14] 6.346 0.526 5.320 6.327 7.388
beta1_dsr[15] 3.321 0.267 2.800 3.320 3.841
beta1_dsr[16] 5.803 0.369 5.084 5.803 6.546
beta2_dsr[11] -8.330 2.382 -13.879 -7.923 -4.682
beta2_dsr[12] -7.070 2.618 -12.532 -6.904 -2.335
beta2_dsr[13] -6.422 2.742 -12.196 -6.392 -1.353
beta2_dsr[14] -6.116 2.775 -12.427 -5.976 -1.745
beta2_dsr[15] -7.820 2.423 -13.377 -7.498 -3.976
beta2_dsr[16] -8.050 2.377 -13.374 -7.704 -4.399
beta3_dsr[11] 43.491 0.150 43.214 43.487 43.772
beta3_dsr[12] 33.974 0.729 32.195 34.131 34.795
beta3_dsr[13] 43.240 0.287 42.816 43.178 43.848
beta3_dsr[14] 43.358 0.249 43.078 43.283 43.980
beta3_dsr[15] 43.513 0.184 43.172 43.511 43.854
beta3_dsr[16] 43.438 0.158 43.172 43.422 43.756
beta4_dsr[11] 0.590 0.210 0.187 0.584 1.013
beta4_dsr[12] 0.245 0.433 -0.577 0.240 1.104
beta4_dsr[13] -0.174 0.214 -0.596 -0.174 0.234
beta4_dsr[14] 0.150 0.244 -0.328 0.148 0.625
beta4_dsr[15] 0.726 0.210 0.333 0.720 1.147
beta4_dsr[16] 0.133 0.219 -0.305 0.137 0.557
beta0_slope[11] -1.939 0.161 -2.250 -1.939 -1.625
beta0_slope[12] -4.654 0.259 -5.173 -4.654 -4.159
beta0_slope[13] -1.343 0.202 -1.775 -1.330 -0.994
beta0_slope[14] -2.644 0.176 -2.978 -2.646 -2.299
beta0_slope[15] -1.389 0.162 -1.706 -1.388 -1.079
beta0_slope[16] -2.721 0.171 -3.047 -2.722 -2.386
beta1_slope[11] 4.592 0.297 4.012 4.591 5.183
beta1_slope[12] 5.000 0.522 4.003 5.000 6.044
beta1_slope[13] 2.928 0.505 2.216 2.862 4.264
beta1_slope[14] 6.523 0.565 5.471 6.512 7.641
beta1_slope[15] 3.056 0.285 2.511 3.057 3.618
beta1_slope[16] 5.361 0.385 4.624 5.359 6.139
beta2_slope[11] 7.972 2.322 4.480 7.650 13.342
beta2_slope[12] 7.093 2.529 2.669 6.787 12.666
beta2_slope[13] 5.545 2.863 0.402 5.680 11.358
beta2_slope[14] 6.493 2.453 2.378 6.301 11.984
beta2_slope[15] 7.332 2.236 3.624 7.051 12.540
beta2_slope[16] 7.629 2.423 3.816 7.246 13.486
beta3_slope[11] 43.477 0.149 43.201 43.479 43.765
beta3_slope[12] 43.412 0.232 43.056 43.386 43.870
beta3_slope[13] 43.616 0.431 42.910 43.681 44.245
beta3_slope[14] 43.319 0.177 43.095 43.275 43.775
beta3_slope[15] 43.507 0.193 43.164 43.502 43.863
beta3_slope[16] 43.458 0.169 43.179 43.442 43.797
beta4_slope[11] -0.573 0.213 -0.982 -0.578 -0.160
beta4_slope[12] -1.384 0.647 -2.848 -1.306 -0.346
beta4_slope[13] 0.050 0.221 -0.375 0.046 0.499
beta4_slope[14] -0.172 0.261 -0.670 -0.178 0.352
beta4_slope[15] -0.712 0.211 -1.136 -0.717 -0.303
beta4_slope[16] -0.191 0.226 -0.638 -0.192 0.255
sigma_H[1] 0.197 0.054 0.100 0.195 0.316
sigma_H[2] 0.171 0.030 0.119 0.169 0.237
sigma_H[3] 0.196 0.042 0.124 0.194 0.289
sigma_H[4] 0.418 0.079 0.289 0.408 0.598
sigma_H[5] 0.995 0.211 0.612 0.979 1.447
sigma_H[6] 0.401 0.199 0.041 0.389 0.823
sigma_H[7] 0.300 0.060 0.205 0.292 0.437
sigma_H[8] 0.416 0.090 0.278 0.406 0.612
sigma_H[9] 0.525 0.126 0.328 0.509 0.817
sigma_H[10] 0.214 0.042 0.142 0.212 0.306
sigma_H[11] 0.279 0.047 0.201 0.275 0.382
sigma_H[12] 0.434 0.164 0.209 0.405 0.771
sigma_H[13] 0.215 0.037 0.149 0.211 0.299
sigma_H[14] 0.508 0.092 0.347 0.503 0.700
sigma_H[15] 0.246 0.040 0.179 0.242 0.334
sigma_H[16] 0.223 0.043 0.152 0.218 0.323
lambda_H[1] 3.029 3.910 0.150 1.765 12.899
lambda_H[2] 8.437 8.096 0.805 6.131 29.394
lambda_H[3] 6.016 9.092 0.262 2.949 29.506
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 4.252 8.435 0.036 1.140 30.842
lambda_H[6] 8.225 15.769 0.007 1.202 53.299
lambda_H[7] 0.013 0.010 0.002 0.011 0.038
lambda_H[8] 8.417 10.613 0.119 4.679 38.497
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.299 0.440 0.033 0.194 1.108
lambda_H[11] 0.262 0.352 0.011 0.132 1.211
lambda_H[12] 4.849 6.347 0.180 2.736 23.087
lambda_H[13] 3.521 3.292 0.252 2.657 12.116
lambda_H[14] 3.258 4.205 0.211 1.999 15.095
lambda_H[15] 0.025 0.032 0.003 0.017 0.092
lambda_H[16] 0.861 1.157 0.045 0.476 3.971
mu_lambda_H[1] 4.276 1.876 1.255 4.093 8.426
mu_lambda_H[2] 3.874 1.908 0.689 3.743 7.917
mu_lambda_H[3] 3.477 1.871 0.743 3.166 7.741
sigma_lambda_H[1] 8.527 4.328 2.097 7.892 18.175
sigma_lambda_H[2] 8.457 4.595 1.210 7.980 18.263
sigma_lambda_H[3] 6.237 4.041 0.906 5.368 16.211
beta_H[1,1] 6.907 1.071 4.410 7.077 8.555
beta_H[2,1] 9.877 0.485 8.791 9.908 10.759
beta_H[3,1] 7.979 0.809 6.016 8.082 9.304
beta_H[4,1] 9.460 7.861 -7.237 9.813 24.403
beta_H[5,1] 0.182 2.287 -4.845 0.365 4.151
beta_H[6,1] 3.148 4.076 -6.851 4.665 7.791
beta_H[7,1] 0.703 5.896 -12.376 1.133 11.255
beta_H[8,1] 1.359 3.962 -2.295 1.227 3.461
beta_H[9,1] 13.107 5.633 1.804 13.038 24.068
beta_H[10,1] 7.042 1.707 3.411 7.136 10.218
beta_H[11,1] 5.219 3.520 -2.737 5.987 10.042
beta_H[12,1] 2.610 1.083 0.828 2.539 4.972
beta_H[13,1] 9.070 0.903 7.154 9.133 10.523
beta_H[14,1] 2.213 1.059 0.087 2.209 4.300
beta_H[15,1] -6.029 3.726 -12.660 -6.245 2.149
beta_H[16,1] 3.334 2.601 -0.851 3.038 9.409
beta_H[1,2] 7.905 0.247 7.412 7.912 8.373
beta_H[2,2] 10.025 0.136 9.757 10.023 10.290
beta_H[3,2] 8.948 0.201 8.548 8.951 9.344
beta_H[4,2] 3.538 1.509 0.765 3.459 6.780
beta_H[5,2] 1.960 0.963 -0.018 1.983 3.790
beta_H[6,2] 5.747 1.070 3.205 5.944 7.357
beta_H[7,2] 2.592 1.140 0.580 2.508 5.008
beta_H[8,2] 3.013 1.116 1.380 3.159 4.247
beta_H[9,2] 3.522 1.085 1.493 3.505 5.820
beta_H[10,2] 8.195 0.355 7.454 8.208 8.872
beta_H[11,2] 9.758 0.630 8.804 9.634 11.191
beta_H[12,2] 3.946 0.383 3.240 3.930 4.718
beta_H[13,2] 9.123 0.249 8.677 9.109 9.631
beta_H[14,2] 4.028 0.363 3.322 4.018 4.760
beta_H[15,2] 11.346 0.674 9.939 11.372 12.582
beta_H[16,2] 4.507 0.797 3.002 4.499 6.126
beta_H[1,3] 8.462 0.240 8.024 8.449 8.957
beta_H[2,3] 10.069 0.118 9.842 10.067 10.299
beta_H[3,3] 9.619 0.167 9.291 9.617 9.960
beta_H[4,3] -2.499 0.888 -4.270 -2.503 -0.795
beta_H[5,3] 3.808 0.614 2.567 3.807 5.002
beta_H[6,3] 7.990 1.181 6.378 7.619 10.596
beta_H[7,3] -2.701 0.752 -4.204 -2.704 -1.221
beta_H[8,3] 5.248 0.509 4.630 5.182 6.218
beta_H[9,3] -2.861 0.727 -4.298 -2.868 -1.451
beta_H[10,3] 8.696 0.280 8.167 8.697 9.260
beta_H[11,3] 8.544 0.280 7.942 8.563 9.030
beta_H[12,3] 5.245 0.332 4.452 5.290 5.774
beta_H[13,3] 8.849 0.175 8.492 8.851 9.181
beta_H[14,3] 5.714 0.277 5.120 5.735 6.201
beta_H[15,3] 10.380 0.316 9.769 10.380 10.998
beta_H[16,3] 6.310 0.583 5.061 6.376 7.284
beta_H[1,4] 8.271 0.173 7.891 8.283 8.578
beta_H[2,4] 10.129 0.117 9.877 10.134 10.351
beta_H[3,4] 10.109 0.165 9.750 10.119 10.400
beta_H[4,4] 11.794 0.450 10.858 11.814 12.648
beta_H[5,4] 5.447 0.745 4.266 5.360 7.184
beta_H[6,4] 7.054 0.957 4.837 7.360 8.348
beta_H[7,4] 8.213 0.362 7.511 8.218 8.926
beta_H[8,4] 6.710 0.253 6.263 6.718 7.133
beta_H[9,4] 7.197 0.466 6.259 7.197 8.088
beta_H[10,4] 7.747 0.233 7.316 7.742 8.239
beta_H[11,4] 9.389 0.202 8.999 9.387 9.782
beta_H[12,4] 7.143 0.219 6.714 7.137 7.599
beta_H[13,4] 9.052 0.141 8.773 9.053 9.315
beta_H[14,4] 7.734 0.220 7.294 7.732 8.175
beta_H[15,4] 9.465 0.235 9.000 9.465 9.928
beta_H[16,4] 9.327 0.232 8.894 9.319 9.790
beta_H[1,5] 8.980 0.147 8.671 8.982 9.263
beta_H[2,5] 10.780 0.093 10.599 10.777 10.969
beta_H[3,5] 10.922 0.176 10.607 10.914 11.291
beta_H[4,5] 8.384 0.474 7.485 8.375 9.349
beta_H[5,5] 5.402 0.574 4.064 5.451 6.377
beta_H[6,5] 8.823 0.635 7.936 8.657 10.342
beta_H[7,5] 6.796 0.340 6.138 6.790 7.492
beta_H[8,5] 8.216 0.219 7.853 8.202 8.610
beta_H[9,5] 8.215 0.476 7.263 8.220 9.147
beta_H[10,5] 10.087 0.227 9.611 10.086 10.529
beta_H[11,5] 11.507 0.235 11.023 11.509 11.957
beta_H[12,5] 8.481 0.200 8.085 8.479 8.889
beta_H[13,5] 10.016 0.132 9.753 10.017 10.275
beta_H[14,5] 9.205 0.235 8.758 9.197 9.683
beta_H[15,5] 11.167 0.247 10.684 11.165 11.659
beta_H[16,5] 9.918 0.178 9.554 9.923 10.251
beta_H[1,6] 10.183 0.188 9.860 10.167 10.616
beta_H[2,6] 11.514 0.108 11.294 11.515 11.723
beta_H[3,6] 10.804 0.163 10.457 10.814 11.090
beta_H[4,6] 12.890 0.822 11.248 12.910 14.488
beta_H[5,6] 5.914 0.593 4.757 5.904 7.039
beta_H[6,6] 8.768 0.703 6.842 8.904 9.770
beta_H[7,6] 9.806 0.562 8.677 9.814 10.897
beta_H[8,6] 9.515 0.290 9.018 9.533 9.964
beta_H[9,6] 8.487 0.795 6.940 8.474 10.027
beta_H[10,6] 9.512 0.310 8.830 9.533 10.070
beta_H[11,6] 10.825 0.346 10.066 10.851 11.451
beta_H[12,6] 9.366 0.254 8.875 9.361 9.898
beta_H[13,6] 11.045 0.165 10.753 11.035 11.395
beta_H[14,6] 9.821 0.288 9.233 9.836 10.361
beta_H[15,6] 10.844 0.429 9.983 10.847 11.673
beta_H[16,6] 10.533 0.236 10.011 10.544 10.971
beta_H[1,7] 10.866 0.875 8.683 10.978 12.251
beta_H[2,7] 12.216 0.428 11.332 12.221 13.051
beta_H[3,7] 10.523 0.668 8.983 10.595 11.635
beta_H[4,7] 2.449 4.135 -5.507 2.334 10.767
beta_H[5,7] 6.449 1.799 3.211 6.403 10.319
beta_H[6,7] 9.719 2.551 4.809 9.582 16.235
beta_H[7,7] 10.774 2.781 5.368 10.744 16.277
beta_H[8,7] 10.944 1.110 9.368 10.897 12.494
beta_H[9,7] 4.423 4.064 -3.630 4.439 12.468
beta_H[10,7] 9.791 1.458 7.064 9.711 12.991
beta_H[11,7] 10.944 1.670 7.778 10.825 14.563
beta_H[12,7] 9.973 0.994 7.756 10.065 11.549
beta_H[13,7] 11.677 0.751 9.910 11.772 12.850
beta_H[14,7] 10.402 0.972 8.254 10.472 12.075
beta_H[15,7] 11.972 2.220 7.731 11.918 16.285
beta_H[16,7] 12.265 1.243 10.248 12.084 15.127
beta0_H[1] 8.803 13.799 -19.802 8.817 36.859
beta0_H[2] 10.629 6.336 -2.726 10.505 23.805
beta0_H[3] 10.120 10.197 -10.051 10.046 30.429
beta0_H[4] 7.939 182.898 -355.582 5.727 408.314
beta0_H[5] 3.863 26.156 -44.024 4.206 49.437
beta0_H[6] 6.755 49.687 -101.991 7.366 116.348
beta0_H[7] 6.353 134.720 -261.170 5.676 275.687
beta0_H[8] 6.587 27.765 -15.433 6.332 28.695
beta0_H[9] 4.943 127.057 -243.742 6.719 249.590
beta0_H[10] 8.375 34.299 -58.140 8.320 77.234
beta0_H[11] 8.522 48.632 -94.327 9.434 111.099
beta0_H[12] 6.663 11.726 -14.961 6.617 28.638
beta0_H[13] 9.445 11.321 -12.746 9.661 29.023
beta0_H[14] 6.977 12.128 -16.686 7.098 30.980
beta0_H[15] 9.256 108.576 -214.664 8.863 234.318
beta0_H[16] 8.061 26.003 -43.224 7.805 59.740